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Question

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2 y=\frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $\mathrm{C}$, makes an angle of $\frac{\pi}{4}$ with the line $\mathrm{CP}$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $P Q R$ (in unit $^{2}$ ) is :

2
2$\sqrt2$
$8 \sin \left(\frac{\pi}{8}\right)$
$8 \cos \left(\frac{\pi}{8}\right)$

Solution

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